ABSTRACT

A deep-learning approach is proposed to predict an optimized high-resolution structure with multi-boundary conditions. An enhanced deep super-resolution (SR) neural network and a convolutional neural network are constructed and trained to establish the mapping relationship between low- and high-resolution structures for the topology optimization problem. The data set for training and testing is generated using the solid isotropic material with penalization method, in which the training and test sets have different geometric boundary conditions. Each sample contains both low- and high-resolution structures. The deep neural network is trained with limited training samples (4000), and numerical experiments demonstrate that the proposed method can obtain an accurate high-resolution structure in negligible computational time. Moreover, the proposed method has the generalization ability necessary to predict high-resolution structures with multi-geometric boundary conditions. The effective incorporation of a deep SR neural network and topology optimization has enormous potential for future practical applications in large-scale structural design.

摘要

提出了一种深度学习方法来预测具有多边界条件的优化高分辨率结构。构建并训练增强型深度超分辨率 (SR) 神经网络和卷积神经网络，以建立拓扑优化问题的低分辨率和高分辨率结构之间的映射关系。用于训练和测试的数据集是使用带有惩罚方法的固体各向同性材料生成的，其中训练集和测试集具有不同的几何边界条件。每个样本都包含低分辨率和高分辨率结构。深度神经网络使用有限的训练样本（4000）进行训练，数值实验表明所提出的方法可以在可以忽略不计的计算时间内获得准确的高分辨率结构。而且，所提出的方法具有预测具有多几何边界条件的高分辨率结构所必需的泛化能力。深度 SR 神经网络和拓扑优化的有效结合对于未来大规模结构设计的实际应用具有巨大的潜力。